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The halo concentration-mass relation has ubiquitous use in modeling thematter field for cosmological and astrophysical analyses, and including theimprints from galaxy formation physics is tantamount to its robust usage. Manyanalyses, however, probe the matter around halos selected by a givenhalo/galaxy property -- rather than by halo mass -- and the imprints under eachselection choice can be different. We employ the CAMELS simulation suite toquantify the astrophysics and cosmology dependence of the concentration-massrelation, $c_{\rm vir}-M_{\rm vir}$, when selected on five properties: (i)velocity dispersion, (ii) formation time, (iii) halo spin, (iv) stellar mass,and (v) gas mass. We construct simulation-informed nonlinear models for allproperties as a function of halo mass, redshift, and sixcosmological/astrophysical parameters, with a mass range $M_{\rm vir} \in[10^{11}, 10^{14.5}] M_\odot/h$. There are many mass-dependent imprints in allhalo properties, with clear connections across different properties andnon-linear couplings between the parameters. Finally, we extract the $c_{\rmvir}-M_{\rm vir}$ relation for subsamples of halos that have scatteredabove/below the mean property-$M_{\rm vir}$ relation for a chosen property.Selections on gas mass or stellar mass have a significant impact on theastrophysics/cosmology dependence of $c_{\rm vir}$, while those on any of theother three properties have a significant (mild) impact on the cosmology(astrophysics) dependence. We show that ignoring such selection effects canlead to errors of $\approx 25\%$ in baryon imprint modelling of $c_{\rm vir}$.Our nonlinear model for all properties is made publicly available.

Baryonic Imprints on DM Halos: the concentration-mass relation and its dependence on halo and galaxy properties